论文标题
模块化高斯曲率背后的循环结构
Cyclic Structure behind Modular Gaussian Curvature
论文作者
论文摘要
我们提出了一个系统的方案，用于计算在非交通性Tori和$θ$成型的Riemannian歧管上最近开发的光谱几何形状中产生的重排算子的变化。它可以概括为一个类别，其对象由重排操作员的光谱函数组成，并且形态是由与变异算术基本操作相关的转换而产生的。形态的发生器满足了Connes循环类别中的大多数关系，但也包括所有部分衍生物。还与HOPF循环理论进行了比较。
We propose a systematic scheme for computing the variation of rearrangement operators arising in the recently developed spectral geometry on noncommutative tori and $θ$-deformed Riemannian manifolds. It can be summarized as a category whose objects consists of spectral functions of the rearrangement operators and morphisms are generated by transformations associated to basic operations of the variational calculus. The generators of the morphisms fulfil most of the relations in Connes's cyclic category, but also include all the partial derivatives. Comparison with Hopf cyclic theory has also been made.
